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Approximate methods for optimal replacement, maintenance, and inspection policies

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  • Zhao, Xufeng
  • Al-Khalifa, Khalifa N.
  • Nakagawa, Toshio

Abstract

It might be difficult sometimes to derive theoretical and numerical solutions for analytical maintenance modelings due to the computational complexity. This paper takes up several approximate models in maintenance theory, by using the cumulative hazard function H(t) and the newly proposed asymptotic MTTF (Mean Time to Failure) skilfully. We firstly denote by tx the time when the expected number of failures is x. Using H(tx)=x, we estimate failure times, model age and periodic replacements, and sequential imperfect maintenance. Motivated by the asymptotic method of computation of MTTF, we secondly model the expected cost rate for a parallel system when replacement is made at system failure, and give approximate computations for the sequential inspection policy. Optimizations of each model are obtained approximately in an easier way. When failure times have a Weibull distribution, it is shown from numerical examples that the obtained approximate optimal solutions have good approximations of the exact ones.

Suggested Citation

  • Zhao, Xufeng & Al-Khalifa, Khalifa N. & Nakagawa, Toshio, 2015. "Approximate methods for optimal replacement, maintenance, and inspection policies," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 68-73.
    • Handle: RePEc:eee:reensy:v:144:y:2015:i:c:p:68-73
    DOI: 10.1016/j.ress.2015.07.005
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    References listed on IDEAS

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    1. Jiang, R., 2009. "An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1245-1250.
    2. Riccardo Manzini & Alberto Regattieri & Hoang Pham & Emilio Ferrari, 2010. "Maintenance for Industrial Systems," Springer Series in Reliability Engineering, Springer, number 978-1-84882-575-8, February.
    3. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, February.
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    1. Zhao, Xufeng & Chen, Mingchih & Nakagawa, Toshio, 2016. "Replacement policies for a parallel system with shortage and excess costs," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 89-95.
    2. Zhao, Xufeng & Al-Khalifa, Khalifa N. & Magid Hamouda, Abdel & Nakagawa, Toshio, 2017. "Age replacement models: A summary with new perspectives and methods," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 95-105.
    3. Tsai, Hsin-Nan & Sheu, Shey-Huei & Zhang, Zhe George, 2017. "A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 74-88.
    4. Shen, Jingyuan & Cui, Lirong & Ma, Yizhong, 2019. "Availability and optimal maintenance policy for systems degrading in dynamic environments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 133-143.
    5. Tsai, Hsin-Nan & Sheu, Shey-Huei & Zhang, Zhe George, 2017. "A trivariate optimal replacement policy for a deteriorating system based on cumulative damage and inspections," Reliability Engineering and System Safety, Elsevier, vol. 160(C), pages 122-135.
    6. Junyuan Wang & Jimin Ye, 2022. "A new repair model and its optimization for cold standby system," Operational Research, Springer, vol. 22(1), pages 105-122, March.
    7. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    8. Hajipour, Yassin & Taghipour, Sharareh, 2016. "Non-periodic inspection optimization of multi-component and k-out-of-m systems," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 228-243.

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